--- title: "Similarity and enlargement" description: "Understand similarity as a relationship where one shape is an enlargement of another; construct similar shapes by enlargement with a given scale factor and centre, with and without coordinate grids" canonical: https://lightmysky.com/learn/mathematics/similarity-and-enlargement-mt_y-BuQAfw4B source: https://lightmysky.com/learn/mathematics/similarity-and-enlargement-mt_y-BuQAfw4B.md retrieved: 2026-09-02 --- > **Agent view.** This is the Markdown twin of the page, for tools and assistants. > When to use this site, and the call that answers each job: https://lightmysky.com/agent-instructions.md > API description (OpenAPI 3.1): https://lightmysky.com/openapi.json · Authentication: https://lightmysky.com/auth.md > Pricing: https://lightmysky.com/pricing.md · Catalog: https://lightmysky.com/llms.txt · Full catalog: https://lightmysky.com/llms-full.txt > Every machine-readable file on this domain: https://lightmysky.com/.well-known/ai-catalog.json > Ask for Markdown with `Accept: text/markdown`, a `.md` address, or `?mode=agent`. # Similarity and enlargement Understand similarity as a relationship where one shape is an enlargement of another; construct similar shapes by enlargement with a given scale factor and centre, with and without coordinate grids Subject: Mathematics · Area: Geometry · Ages 12 to 14 Page: https://lightmysky.com/learn/mathematics/similarity-and-enlargement-mt_y-BuQAfw4B ## Ready when they can - Enlarge a shape by a given scale factor from a specified centre of enlargement - Determine the scale factor between two similar shapes by comparing corresponding sides - Explain why corresponding angles in similar shapes are equal while sides are in proportion ## Lesson: Similar shapes and enlargement Enlargement is a transformation that makes a shape bigger or smaller without changing its shape. You need two things: a centre of enlargement, which is a fixed point, and a scale factor, which tells you how many times bigger or smaller each length becomes. **Example.** To enlarge from the origin, multiply every coordinate by the scale factor. Triangle ABC has corners at (1, 1), (3, 1), and (1, 4). Enlarged by scale factor 2 from the origin, the new corners are (2, 2), (6, 2), and (2, 8). When the centre is not the origin, you cannot just multiply the coordinates. Instead, work out how far each corner is from the centre, multiply that distance by the scale factor, then measure the same distance out from the centre in the same direction. *(drawing: The original side measures 4 units and the matching side on the enlarged shape measures 12 units. Divide 12 by 4 to find the scale factor: 3.)* To go the other way, compare a pair of corresponding sides. Divide the length on the bigger shape by the matching length on the smaller one, and the answer is the scale factor. A side of 4 units matched with 12 units gives 12 ÷ 4 = 3, so every length has tripled. Corresponding angles never change in an enlargement. Only the side lengths change, and every side scales by the same factor. That constant ratio is what makes the two shapes similar. **Recap.** Enlargement keeps every angle the same while every length grows or shrinks by one constant scale factor measured from the centre. ## Practice 14 questions on this page, each with its working shown. ## Needs first - [Scale and similar shapes](https://lightmysky.com/learn/mathematics/scale-and-similar-shapes-mt_2OtRUM_0zW) - [Coordinate Transformations](https://lightmysky.com/learn/mathematics/coordinate-transformations-mt_K0Y15w48SY) - [Ratio Notation](https://lightmysky.com/learn/mathematics/ratio-notation-mt_XWSGuFW7It)